Which of the following numbers is a factor of 152? ${3,8,9,10,12}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $152$ by each of our answer choices. $152 \div 3 = 50\text{ R }2$ $152 \div 8 = 19$ $152 \div 9 = 16\text{ R }8$ $152 \div 10 = 15\text{ R }2$ $152 \div 12 = 12\text{ R }8$ The only answer choice that divides into $152$ with no remainder is $8$ $ 19$ $8$ $152$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $8$ are contained within the prime factors of $152$ $152 = 2\times2\times2\times19 8 = 2\times2\times2$ Therefore the only factor of $152$ out of our choices is $8$. We can say that $152$ is divisible by $8$.